Given a 3–manifold the second author defined functions , generalizing McMullen’s Alexander norm, which give lower bounds on the Thurston norm. We reformulate these invariants in terms of Reidemeister torsion over a non-commutative multivariable Laurent polynomial ring. This allows us to show that these functions are semi-norms.
"Non-commutative multivariable Reidemester torsion and the Thurston norm." Algebr. Geom. Topol. 7 (2) 755 - 777, 2007. https://doi.org/10.2140/agt.2007.7.755